The Rupture Rule and the Layer Count Law

The BPT law

BPT Chapter 1 opens with the Recursive Growth Law: "Each completed pulse holds everything before it and as much again: ℜ(n) = 2ⁿ." Part D.3 makes it two-sided. "On the UniSphere side it counts levels: the capacity available to a universe at level L is ℜ_U(L) = 2^L. On the universe side it counts that universe's own completed pulses: ℜ(n) = 2ⁿ." Where the two meet is the Rupture Rule, n↯ = 2^L: "A universe spawns when its own pulse count reaches the UniSphere's capacity at its level." n↯ counts "completed Pulse Tempos of the universe, full 0 → 1 → 0 cycles rather than single flips". Solving for L from the Rupture Rule gives L = log₂(t↯/①⥂⧗⌂). The book's candidate signature for ours is 2²⁰²·①⥂⧗⌂ = 11.0 Gyr, beside the dark-energy–matter equality near 10.2 Gyr (Part D.4).

BPT Part 3.6 counts the layers of that life. The Layer Count Law is h⥣(L) = 3 · 2^L: "A universe of level L reaches Harmonic 3·2^L before its final well; the last harmonics arrive together as its life closes." The life is counted from the Physical Nova, Harmonic 3, the big bang: "Counted from the Physical Nova, Harmonic h arrives at t_h = (1 − 3/h) · 2ᴸ Tempos: spacetime (h = 4) at a quarter of the life, h = 6 at a half, h = 12 at three quarters." Before it, "the data's count goes on past the Data Nova ... to Harmonic 3 at (1 − 2/3)·2^L = 2^L / 3 of its Tempos", and that count "takes no time on the universe's clock". (The code comment of 2026-10-28 records the correction from 2^(L+1), when the life was counted from the Data Nova.)

The established physics

None: a game method resting on BPT. The book compares 2²⁰²·t_p ≈ 11.0 Gyr with the dark-energy–matter equality near 10.2 Gyr as its candidate signature. That is a BPT prediction, not established physics.

The game's math

• growth(n) universe.js:242 = 2ⁿ for n ≥ 0, else 0. It is used only by the tests.
• rupturePulses(L) universe.js:245 = 2^L. ruptureTime = 2^L·Tempo (universe.js:314).
• layerCeiling(L) universe.js:249 = 3·2^L.
• levelFromRuptureTime(t) universe.js:265 = log₂(t/t_p). It is used only by the tests. The book rounds; the function does not.

At level 28 the universe lives 2²⁸ = 268,435,456 Tempos (2.55 × 10⁻⁸⁹ s) and reaches Harmonic 3·2²⁸ = 805,306,368. At ours, 2²⁰² = 6.43 × 10⁶⁰ Tempos = 10.98 Gyr.

The game's own clock runs in Tempos since the Data Nova. physicalTempo() app.js:4282 places the big bang at ceil(rupturePulses/3). The final well comes at physicalTempo() + rupturePulses (lifeEndTempo()), and harmonicTempo(h) places Harmonic h ≥ 4 at physicalTempo() + ceil(rupturePulses·(1 − 3/h)). All three read uni.rupturePulses, which scaleModel() has replaced with the model's 2^Lm (Part 1.10). The main loop calls rupture() when universePulses() ≥ lifeEndTempo() (app.js:4581). Chapter 3 of this book covers the novas.

In the game

This law is the shape of a run. The readout card states it before Start: "Rupture at 2.684 × 10⁸ Tempos" ("Rupture Rule: n = 2^L full cycles") and "Layers up to 8.053 × 10⁸" ("Layer Count Law: h_max = 3·2^L, counted from the big bang") at level 28 (app.js:2084–2085). The About panel's "Two clocks" card (index.php:305) says "Your Tempos count toward 2^L, the UniSphere's capacity at your level."

During the run the HUD follows the life (app.js:2124–2136):

• "Tempos:" (tooltip "Own Pulse Tempos (full 0 → 1 → 0 cycles) out of 2^L, the Rupture Rule") reads "data within … of the skin's … bits" while the Pulsecore fills, then "the data's count 12 / 22 · beyond time" between the Data Nova and the big bang, and "37 / 64 since the big bang" afterwards on a level-6 model. The words "beyond time" carry the theory's point that the data's count takes no time on the universe's clock.
• "Capacity:" gives the share of 2^L used, and the bar under the HUD ("Progress to rupture", index.php:90) fills with it.
• "Epoch:" reads "pre-pulse", "processing", "toward the final well", "final well formed", "returning to the Source" and "returned to the Source".
• "Layer:" reads "3 of 192 · Harmonic 3 · Temporal Genesis · physical" (updateLayerHud() app.js:2113).

When the count reaches the end of the life, rupture() runs. The state line reads "State: Final well" (app.js:2569), and a banner rises with "Final well · N wells", "Returning to the Source" and "its last bits pass home through its wells · 40%", the share counting up as the field dims (returnBanner() app.js:2588). The end card then opens "Your universe lived 2.684 × 10⁸ Pulses, formed its final well, and its data returned through its wells to the Source" and shows "Pulses lived" ("from its big bang to its final well (the Rupture Rule, 2^28)") and "Harmonics" (app.js:2776–2777).

The scale model

The true counts are kept as uni.trueRupture and uni.trueLayers (app.js:4247). They appear in the readout rows "Rupture at" and "Layers" (app.js:2084–2085) and on the end card ("Pulses lived" and "Harmonics", app.js:2765, 2770). The run itself is played at 2^Lm Tempos and 3·2^Lm harmonics, which is why the HUD's "Tempos" and "Layer" lines count to 64 and 192 on a desktop at any level past 6. The end card scales the harmonics reached in proportion: round(trueLayers × novaCount / layers) (app.js:2770). Its "Pulses lived" line adds "as a level 6 model" when the model is shallower than the level.

Where the game and the theory differ

• The HUD's "Layer" tooltip (index.php:76) still says "out of the Layer Count Law's 2^(L+1)". BPT Part 3.6 and the code both use 3·2^L.
• On the end card's "Harmonics" line (app.js:2777), the text "its Pulsecore 4·2^L cells across (16·4^L)" puts a side length next to the pixel-count formula. The number is the side, 4·2^L. 16·4^L is the area.
• BPT writes L = round(log₂(t↯/①⥂⧗⌂)) in its testable predictions and in Part 1.9. levelFromRuptureTime() does not round.

Fixed numbers